﻿94 
  

  

  Errors 
  in 
  Ruling 
  a 
  Diffraction 
  Grating. 
  

  

  is 
  the 
  left 
  — 
  of 
  the 
  central 
  image, 
  the 
  results 
  as 
  here 
  expressed 
  

   are 
  exactly 
  reversed"*. 
  

  

  If 
  the 
  change 
  in 
  the 
  ruling 
  is 
  gradual, 
  instead 
  of 
  sudden, 
  

   we 
  should 
  have 
  to 
  consider 
  a 
  series 
  of 
  focal 
  points 
  F, 
  but 
  the 
  

   same 
  line 
  of 
  reasoning 
  may 
  be 
  followed. 
  

  

  ruling 
  in 
  

  

  The 
  conclusions 
  may 
  be 
  summarized 
  as 
  follows 
  :- 
  

  

  Orders 
  on 
  the 
  right 
  of 
  the 
  Central 
  Image. 
  

  

  Case 
  1. 
  — 
  In 
  passing 
  from 
  a 
  wide 
  to 
  a 
  narrow 
  

   going 
  from 
  left 
  to 
  right. 
  

  

  Focus 
  in. 
  Light 
  band. 
  

  

  Focus 
  out. 
  Dark 
  band. 
  

  

  * 
  If 
  light 
  of 
  wave-length 
  X 
  falls 
  at 
  normal 
  incidence 
  on 
  a 
  grating 
  ruled 
  

   with 
  N 
  lines 
  per 
  unit-length 
  and 
  is 
  diffracted 
  at 
  an 
  angle 
  0, 
  

  

  sin 
  6 
  = 
  ?iXN, 
  

   86 
  = 
  n\8N/cos0, 
  

  

  where 
  n 
  is 
  the 
  order 
  of 
  the 
  spectrum. 
  

  

  The 
  distance 
  F, 
  F 
  2 
  is 
  fdtf 
  where 
  / 
  is 
  the 
  local 
  length 
  of 
  the 
  lens. 
  

   If 
  the 
  distance 
  FB' 
  is 
  a, 
  and 
  the 
  distance 
  FB" 
  is 
  b, 
  the 
  amount 
  of 
  over- 
  

   lapping 
  at 
  B" 
  is 
  - 
  . 
  1S6. 
  

  

  